Among equipments used to manufacture semiconductor devices, a plasma apparatus is widely used for forming plasma in a closed chamber of vacuum state, depositing a thin film on a wafer by injecting a reaction gas, and etching a thin film formed on a wafer.
The plasma apparatus has various advantages in that when the deposition process is performed using the plasma, the deposition process can be performed in a low temperature which does not allow impurities formed in the wafer to further diffuse, and the thickness uniformity of the thin film formed on a large-sized wafer is excellent, and that when the etch process is performed, the etch uniformity of the thin film across the wafer is excellent. Accordingly, the plasma apparatus is widely used.
A Langmuir probe is most widely used to measure plasma parameters in the plasma of a plasma apparatus and determine plasma characteristics and ion and electron distribution.
There are three types of Langmuir probes: a single Langmuir probe, a double Langmuir probe and a triple Langmuir probe. The Langmuir probe may be used to obtain a current-voltage characteristic curve of the plasma by inserting the probe made from metal in the plasma, applying a voltage to the probe, and measuring a current flowing through the probe.
For example, in the single probe, the current-voltage curve is expressed as Equation (1):
                                          I            P                    =                                    I              +                        -                                          I                -                            ⁢                              exp                ⁡                                  [                                                                                    V                        B                                            -                                              V                        P                                                                                    T                      e                                                        ]                                                                    ,                            (        1        )            where I+, I−, VB, VP are an ion saturation current, an electron saturation current, a probe potential and a plasma potential respectively. That is, as the probe potential increases, the current flowing through the probe increases exponentially.
Also, in the double probe, the current-voltage curve is expressed as Equation (2):
                              I          P                =                              I            +                    ⁢                                    tanh              ⁡                              (                                                      V                    B                                                        2                    ⁢                                          T                      e                                                                      )                                      .                                              (        2        )            
Data such as an ion saturation current, an electron saturation current, an electron temperature, a plasma potential, and the like can be obtained from each of the current-voltage characteristic curves. Such a method is simple, but it has an inconvenience in that the current-voltage curve must be obtained, and that a separate signal processing is required for obtaining this data.
Also, when an insulator layer is formed on the probe surface through the deposition in the plasma, the biggest problem is that the probes cannot operate correctly, whereby the current-voltage curve cannot be obtained. Further, it is the most important requirement that a measurement object in the plasma diagnostic not be influenced by any effects, such as perturbation. However, since many charges in the plasma are extracted, the object is influenced by perturbation. Furthermore, real-time plasma analysis is also difficult.
Meanwhile, while there have been various attempts to diagnose the plasma using the nonlinearity of a plasma sheath, such attempts have failed to obtain satisfactory results. There is a method for measuring an electron temperature approximately using the nonlinearity in a nuclear fusion plasma such as Tokamak.
The method is more specifically explained in below.
After floating the probe inserted into the plasma in a plasma chamber using a DC current blocking capacitor, if a sine-wave voltage is applied, the current flowing through the probe is expressed as Equation (3):ipr=i+−i−exp [(VB−VP)/Te],  (3)
where Ipr is a current flowing through the probe, i+ and i− are an ion saturation current and an electron saturation current respectively, and VB, VP, and Te are a probe potential, a plasma potential and an electron temperature respectively.
i+,i− are expressed as Equation (4) and Equation (5) respectively:i+=0.61e niuBA,  (4)where, ni is an ion density, UB is a Bohm velocity, and A is a probe area. Further, e represents a charge of an electron, as is well known in the art.
                                          i            -                    =                                    1              4                        ⁢                          en              e                        ⁢                          v              e                        ⁢            A                          ,                            (        5        )            where ne is an ion density, and Ve is an electron velocity.
Accordingly, if the probe potential(VB) is VB= V+V0 cos wt, the current flowing through the probe is expressed as Equation (6):
                                          i            pr                    =                                    i              +                        -                                          i                -                            ⁢                              exp                ⁡                                  [                                                            (                                                                        V                          _                                                -                                                  V                          P                                                                    )                                        /                                          T                      e                                                        ]                                            ⁢                              exp                ⁡                                  [                                                                                    V                        0                                                                    T                        e                                                              ⁢                    cos                    ⁢                                                                                  ⁢                    wt                                    ]                                                                    ,                            (        6        )            where V is a floating potential.
If the probe current(ipr) is expanded by a modified Bessel function. The result is expressed as Equation (7):
                                                                        i                pr                            =                            ⁢                                                i                  +                                -                                                      i                    -                                    ⁢                                                            exp                      ⁡                                              [                                                                              (                                                                                          V                                _                                                            -                                                              V                                P                                                                                      )                                                    /                                                      T                            e                                                                          ]                                                              [                                                                                            I                          0                                                ⁡                                                  (                                                                                    V                              0                                                                                      T                              e                                                                                )                                                                    +                                              2                        ⁢                                                                              ∑                                                          k                              =                              1                                                        ∞                                                    ⁢                                                                                                                    I                                k                                                            ⁡                                                              (                                                                                                      V                                    0                                                                                                        T                                    e                                                                                                  )                                                                                      ⁢                                                          cos                              ⁡                                                              (                                                                  k                                  ⁢                                                                                                                                          ⁢                                  ω                                  ⁢                                                                                                                                          ⁢                                  t                                                                )                                                                                                                                                                          ]                                                                                                                          =                            ⁢                                                i                  +                                -                                                      i                    -                                    ⁢                                      exp                    ⁡                                          [                                                                        (                                                                                    V                              _                                                        -                                                          V                              P                                                                                )                                                /                                                  T                          e                                                                    ]                                                        ⁢                                      (                                                                  I                        0                                            ⁡                                              (                                                                              V                            0                                                                                T                            e                                                                          )                                                              )                                                  -                                                                                                      ⁢                                                i                  -                                ⁢                                                      exp                    ⁡                                          [                                                                        (                                                                                    V                              _                                                        -                                                          V                              P                                                                                )                                                /                                                  T                          e                                                                    ]                                                        [                                      2                    ⁢                                                                  ∑                                                  k                          =                          1                                                ∞                                            ⁢                                                                                                    I                            k                                                    ⁡                                                      (                                                                                          V                                0                                                                                            T                                e                                                                                      )                                                                          ⁢                                                  cos                          ⁡                                                      (                                                          k                              ⁢                                                                                                                          ⁢                              ω                              ⁢                                                                                                                          ⁢                              t                                                        )                                                                                                                                ]                                                                                                        =                            ⁢                                                i                  DC                                +                                  i                  AC                                                                                        (        7        )            
As shown by Equation (7), the probe current(ipr) consists of a DC current and an AC current.
As described later, if the probe is connected to the DC current blocking capacitor according to this invention, the DC current cannot flow.
Accordingly, the DC current(iDC) of the probe current(ipr) is expressed as Equation (8):
                              i          DC                =                              i            -                                          i                -                            ⁢                              exp                ⁡                                  [                                                            (                                                                        V                          _                                                -                                                  V                          p                                                                    )                                        /                                          T                      e                                                        ]                                            ⁢                              (                                                      I                    0                                    ⁡                                      (                                                                  V                        0                                                                    T                        e                                                              )                                                  )                                              =          0.                                    (        8        )            
Also, log is applied to Equation (8) and the result is obtained as Equation (9):
                                                        (                                                V                  _                                -                                  V                  p                                            )                                      T              e                                +                      log            ⁡                          (                                                I                  0                                ⁡                                  (                                                            V                      0                                                              T                      e                                                        )                                            )                                      =                              log            ⁡                          (                                                I                  +                                                  I                  -                                            )                                .                                    (        9        )            
The floating potential is the potential between capacitors, and the plasma potential may be obtained from Equation (9) using the floating potential and the electron temperature. Also, the floating potential varies with V0, accordingly, after obtaining the floating potential variation (Δ V) with V0 changes, the electron temperature may be obtained using Equation (9). An approximate calculation equation is expressed as Equation (10):
                                          T            e                    =                                    -                              1                4                                      ⁢                                          V                0                2                                            Δ                ⁢                                                                  ⁢                                  V                  _                                                                    ,                            (        10        )            where Δ V is a floating potential variation.
The AC current is expressed as Equation (11):
                              i          AC                =                                            -                              i                -                                      ⁢                          exp              ⁡                              [                                                      (                                                                  V                        _                                            -                                              V                        P                                                              )                                    /                                      T                    e                                                  ]                                      ⁢                          (                                                2                  ⁢                                                            ∑                                              k                        =                        1                                            ∞                                        ⁢                                                                                            I                          k                                                ⁡                                                  (                                                                                    V                              0                                                                                      T                              e                                                                                )                                                                    ⁢                                              cos                        ⁡                                                  (                                                      k                            ⁢                                                                                                                  ⁢                            ω                            ⁢                                                                                                                  ⁢                            t                                                    )                                                                                                                    +                …                            )                                =                                    -              2                        ⁢                          i              -                        ⁢                          exp              ⁡                              [                                                      (                                                                  V                        _                                            -                                              V                        P                                                              )                                    /                                      T                    e                                                  ]                                      ⁢                                                                           [                                                                                                              I                          1                                                ⁡                                                  (                                                                                    V                              0                                                                                      T                              e                                                                                )                                                                    ⁢                                              cos                        ⁡                                                  (                                                      ω                            ⁢                                                                                                                  ⁢                            t                                                    )                                                                                      +                                                                                            I                          2                                                ⁡                                                  (                                                                                    V                              0                                                                                      T                              e                                                                                )                                                                    ⁢                                              cos                        ⁡                                                  (                                                      2                            ⁢                            ω                            ⁢                                                                                                                  ⁢                            t                                                    )                                                                                      +                                                                                            I                          3                                                ⁡                                                  (                                                                                    V                              0                                                                                      T                              e                                                                                )                                                                    ⁢                                              cos                        ⁡                                                  (                                                      3                            ⁢                            ω                            ⁢                                                                                                                  ⁢                            t                                                    )                                                                                      +                    …                                    ]                                =                                                      -                    2                                    ⁢                                      i                    -                                    ⁢                                                            exp                      ⁡                                              [                                                                              (                                                                                          V                                _                                                            -                                                              V                                P                                                                                      )                                                    /                                                      T                            e                                                                          ]                                                              ⁡                                          [                                                                        i                          ω                                                +                                                  i                                                      2                            ⁢                            ω                                                                          +                                                  i                                                      3                            ⁢                            ω                                                                          +                        …                                            ]                                                                                                                              (        11        )            
Therefore, by comparing between the magnitudes of ω and 2 ω frequency components of the probe current, the result of the comparison is obtained as Equation (12):
                                                        i              ω                                      i                              2                ⁢                ω                                              =                                                                      I                  1                                ⁡                                  (                                                            V                      0                                        /                                          T                      e                                                        )                                                                              I                  2                                ⁡                                  (                                                            V                      0                                        /                                          T                      e                                                        )                                                      ≈                                                            4                  ⁢                                      T                    e                                                                    V                  0                                            ⁢                                                          ⁢                              (                                                      when                    ⁢                                                                                  ⁢                                          V                      0                                                        <                                      T                    e                                                  )                                                    ,                            (        12        )            such that after measuring the magnitudes of ω and 2 ω frequency components, the electron temperature is obtained from Equation (12).
In such a method, in order to measure the electron temperature precisely, it is most important to precisely measure the magnitudes of individual frequency components of the probe current.
Conventionally, after converting a current signal into a voltage signal using a current probe (transformer), two frequency components of the current are obtained using ω and 2 ω Notch filters.